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I'm reading this paper, which uses the quantity $$\max_{x\neq0} \frac{x^T A x}{x^Tx}$$ where $A\in R^{n\times n}$ is nonsingular and $x\in R^n$.
This quantity looks so familiar to me that I'm almost certain this quantity has a special name in linear algebra... Does anyone recognize it or know its name?

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The quantity inside the $\max$ is known as a Rayleigh quotient when $A$ is symmetric (Hermitian). – copper.hat Feb 28 '13 at 20:37
Thanks @copper.hat! I presume that we could also limit our search for a maximum to the unit ball $||x||=1$, correct? – Paul Feb 28 '13 at 20:41
The boundary of the unit ball. (If $A = -I$, then the max would be attained at $x=0$ if you maximized over the unit ball.) – copper.hat Feb 28 '13 at 20:48
up vote 1 down vote accepted

The entire term is the matrix norm of A and the objective function is the Rayleigh quotient.

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